Consider two complex number `z` and `omega` satisfying `|z|= 1` and `|omega-2|+|omega-4|=2`. Then which of the following statements(s) is (are) correct?
A
`Re (z omega)` can never exceed `4`
B
If `argz = argomega`,then `|z+2|`is equal to `3`
C
The minimum value of `|z-omega|` to equal to `2`
D
The maximum value of `|z-omega|` is equal to `6`
Text Solution
Verified by Experts
The correct Answer is:
B
z lies on a unit circle centred at origin and `omega` lies on the line segment joining `(2,0) & (4,0)` ` therefore |z-omega|_("minimum")=BC=1` `&|z-omega|_("maximum") = AD=5` Let `z=e^(itheta)implieszomega ==omega e^(itheta)` where `omega gt 0` `impliesRe(zomega)=omegacostheta le 4` As `argomega = 0 impliesargz = 0` `impliesz "lines at" B(1,0)` `therefore |z+2|=|1+2|=3`
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